[1]} were the first to construct the Gaussian VAR copula via transformation,
but did not recognize it as a Gaussian copula and called it
a “Vector-Autoregressive-To-Anything” distribution. [2]} and [3]}
also consider this Gaussian copula model, its D-vine
representation
and apply
it to multivariate macroeconomic and financial forecasting. Similar
to the univariate case, the Gaussian VAR copula model can capture a degree of
heteroscedasticity in the time series given a suitable choice of marginal distributions
\(G_1,\ldots ,G_d\)  for the \(d\)  time series; see [3]} for a demonstration.
There is also a growing interest in multivariate times series copulas in
machine learning. For example, [5]} construct a Gaussian copula
from low rank factor decomposition where the small number of factors follow a
Gaussian process with recurrent neural network (RNN) dynamics. [6]}
propose constructing a Gaussian copula process that is constructed as
the implicit copula of
an RNN with Gaussian errors.
